Perturb the gyroscope (some ways of doing so are picture below). This can be done by giving a quick push to one of the (red/white) free rings or by picking it up by the stem and moving it around with your hand. One other way of doing this would be to place it on a turntable and set the turntable into motion.

Cautions, Warnings, or Safety Concerns:

N/A

Discussion:

Once the disc is accelerated, it has some amount of angular momentum which is a conserved quantity provided that there exists no net torque on the disc. When one tries to perturb the rotational motion of the disc, the axis of rotation of the disc tends to remain near its original position ("attempting" to conserve its angular momentum). This wobble is a combination of two effects: nutation and precession. Nutation is essentially a wobble of the axis of rotation toward and away from the original axis. Precession is the rotation of the new axis of rotation around the original axis. These are shown in the graphic below.